Counting-based inference of mutant growth rates from pooled sequencing across growth regimes

Simultaneously inferring the growth rates of thousands of genetically distinct cellular variants coexisting in a single culture is now possible by tracking their relative abundances over time through deep sequencing, or other counting methods. This capability provides a quantitative window into increasingly broad regions of the vast combinatorial fitness landscape---well beyond those explored by natural evolution. While identifying a few engineered variants that survive under extreme selection is valuable, quantitative mapping of the fitness landscape requires accurate inference of growth rates for the entire variant population. Here, we revisit three established approaches for estimating growth rates from sequencing count data: least-squares fitting, maximum likelihood estimation, and variational Bayesian inference. In contrast to previous treatments, we introduce the softmax transformation to link the probabilistic model of counting noise to the deterministic model of variant growth. By clearly delineating these two modeling components---jointly required for inferring growth rates from time-resolved sequencing counts---we show how to replace exponential growth with any alternative model defined by a small number of variant-specific parameters. While we illustrate this flexibility using the logistic and Gompertz models of growth, application to more mechanistic models, in which growth rates are expressed in terms of microscopic biochemical parameters, will open the door to high-throughput inference of fundamental kinetic and biophysical constants from sequencing data.